I started to use pikes extensively recently, especially against Khergits, Saranids and other cavalry-heavy factions.
Versus cavalry, the pike really shines. The main reason is the superior reach (bamboo spear can be used in a similar fashion, but I have found no other similar weapon). Skilled cavalrymen are used to the fact that with spears, they usually get the first stab against any footman. With pike, they are wrong - pikeman gets the first stab, and only when screwing up, the rider can kill him.
The key for the pikeman is movement and positioning, so relatively light armor is a must. I usually buy only a pike and some 2h backup weapon for duelling, while picking any discarded shield for emergency missile protection. (Whip out the shield and withdraw).
The essential moment against cav is to maximize the advantage of the weapon length while making aiming difficult for the rider. To do so, I usually wait for the cav to come, then start moving sideways and right before impact forward with a stab. The forward movement is crucial, because the rider is used to time his thrust with the speed of his horse, and by dashing forward, you screw up this timing while gaining nice speed bonus for the pike. If the rider blocks, it's better to stab low, avoiding his shield/weapon, killing or wounding the horse, causing him to rear, otherwise stab high, killing the rider instantly (huge speed bonus). After the horse rears, immediately step back a few steps, avoiding his mad, wild swings or thrusts, prepare the weapon, and move forward stabbing again. Just like with real polearm, this backward-forward movement is crucial. After 2, mostly 3 stabs, the horse usually falls, and with some skill, you can run the rider through before he is able to get up and defend. If he manages to, switch to the backup 2hander and duel him normally.
Against infantry, pike is really unwieldy for duelling. Although you can block if you are good, a skilled duellist will press close and fights you point blank, where he can carve you comfortably while your long weapon is useless for a good riposte. However, pike can be used as a support weapon. Approach a duelling couple and try to stab the enemy combatant - from the right angle, you can at least distract him, offering your team-mate a chance for a kill. Also, if the opponent takes notice and charges, you can frustrate him by running backward and stabbing - the opponent is usually heavier armored and therefore slower, so his swings won't connect, but your stabs will. Feint a stab, causing your opponent to block are reflexively retaliate, but stab quickly again once he opens himself by swinging - though the damage won't probably kill him, you will irritate him to madness. Aim for the head, and you might even score a kill.
Lastly, a pikeman as a support defender - position yourself behind an archer position, ideally in difficult terrain (trees, rocks, houses). Don't stand in front of the archers, you will only hinder their line of sight and draw enemy arrows. Enemy cavalry will usually try to charge the archers with swords or lances - when you see the rider coming, run past the threatened archers and stab the coming horse - riders usually concentrate on their targets, so their response may be slow or improper. If you manage to stab the horse, it will rear, and your archer buddies will nail him with a few arrows, hopefully killing the horse and/or the rider.
Primarily, like in real life battles, pikemen are support, defensive troops - hang around groups of your team-mates, defend archers, stab horses with the pike and let other infantry finish the fallen riders - you won't have so many kills, but you will help your team and your team-mates will appreciate it. A cooperation between a pikeman and an archer can be a powerful combination.
Moreover, a pike is much more tactical weapon than swords and axes. If you find yourself losing in the twitch-fights to all those tricks with super-fast turning-accelerated swings, slash-spams and whole lot of unrealistic elements present in Warband, consider giving the pike a chance. you won't be the dashing hero of the frontline, but your determination and reliability as a support-role infantryman will be surely appreciated by your team.